JP2004244721A - Method for estimating heat transfer coefficient and method for controlling cooling in water-cooling process for steel plate - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain the temperature control having high accuracy by accurately estimating a heat transfer coefficient of a steel plate performing water-cooling treatment in a water-cooling process on-line. <P>SOLUTION: To the steel plate after passing through the water-cooling process, the steel plate temperature during water-cooling and after completing the water-cooling are calculated with the heat transfer calculation by inputting the surface temperature at the inlet side and the outlet side of the water-cooling process, a plate thickness, a plate width, a shifting speed, cooling-water temperature and cooling-water quantity density and the accurate heat transfer coefficient is estimated by using a searching method such as a simulated-annealing method to correct the heat transfer coefficient so that the difference between the above calculated steel plate temperature and the practically measured steel plate temperature becomes little. The optimum water-cooling condition is decided by using the obtained heat transfer coefficient, and repeatedly calculating the steel plate temperature while changing the water-cooling condition. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

  The present invention relates to a cooling control method for a water cooling process in which a moving heated steel plate is cooled with water to a predetermined temperature at a predetermined cooling rate.

In order to accurately control the surface temperature of the steel plate in the water cooling process (hereinafter referred to as plate temperature for simplicity), it is necessary to accurately predict the plate temperature after water cooling. It is necessary to know the heat transfer coefficient between the steel sheet surface and the cooling water. Conventionally, in order to calculate a heat transfer coefficient, it is common to obtain a plate temperature by measuring the plate temperature in a laboratory or the like while cooling the plate with water. It is known that the heat transfer coefficient is generally a function of water cooling conditions such as cooling water density and plate temperature. When calculating in a laboratory or the like as described above, for example, the following non-patent document 1 shows. As it is done, it is necessary to perform measurement under various water cooling conditions.
“Forced cooling of steel”, S53 / 11, Japan Iron and Steel Institute, Part 1 Cooling capacity of various cooling methods for steel. 15

  However, there are many cases where the water cooling conditions such as cooling water density and moving speed, the size of the steel plate, etc. are different between the laboratory and the actual production equipment, and the surface properties of the steel plate (surface roughness, oxide film adhesion, etc.) Since the heat transfer coefficient also changes depending on the temperature, there is a problem that the temperature prediction error and its variation are large when the steel sheet temperature in the actual water cooling process is predicted using the heat transfer coefficient calculated in the laboratory.

  In order to solve the above problem, it is desirable to directly calculate the heat transfer coefficient from actual measurement data and process conditions of the steel sheet to be cooled in the actual water cooling process. However, as described above, the heat transfer coefficient is a function of water cooling conditions such as the surface temperature of the steel sheet and the cooling water density, and the value changes from time to time during the process of cooling the steel sheet. Therefore, if the value of the heat transfer coefficient as a function of the steel sheet surface temperature, cooling water density, etc. is known, the water cooling process outlet temperature after cooling is predicted by performing heat transfer calculation from the start to the end of water cooling. Although it is possible, it is difficult to calculate the heat transfer coefficient only from the outlet side temperature in an actual water cooling process in which it is generally impossible to measure the plate temperature from moment to moment.

  Therefore, the present invention provides a method for accurately estimating the heat transfer coefficient online from measured data and process conditions for a steel sheet that is cooled in an actual water cooling process, to a predetermined temperature at a predetermined cooling rate, It aims at enabling it to cool a steel plate accurately.

The heat transfer coefficient estimation method in the water cooling process of the steel sheet of the present invention adjusts the cooling water density of each cooling zone to obtain a predetermined cooling rate pattern by passing the heated steel sheet through a plurality of cooling zones. In the water cooling process of the steel sheet that is cooled to a predetermined temperature, the actual surface temperature value, the plate thickness, the plate width, the actual moving speed value, and the cooling water temperature in each cooling zone of the steel sheet on the inlet side and the outlet side of the water cooling process. And the cooling water density as input, the steel plate temperature from the start to the end of the water cooling is sequentially calculated by heat transfer for the steel plate after passing through the water cooling process, and the error between the calculated steel plate temperature and the actually measured steel plate temperature. The heat transfer coefficient is calculated by correcting the heat transfer coefficient used in the heat transfer calculation by using a search method so that becomes smaller.
Moreover, the heat transfer coefficient estimation method in the water cooling process of the steel sheet of the present invention is characterized by using a simulated annealing method as a search method.
In addition, the steel sheet cooling control method of the present invention uses the heat transfer coefficient obtained by the above-described heat transfer coefficient estimation method, and changes the water cooling conditions for the steel sheet to be processed in the water cooling process. And the optimal water cooling condition is determined by repeatedly calculating the steel plate temperature after completion | finish, so that the said calculated steel plate temperature may correspond with target temperature.

  As described above, according to the present invention, it is possible to accurately estimate the heat transfer coefficient online from the process conditions and measurement data for the steel sheet subjected to water cooling in the actual water cooling process, and use that value. As a result, the steel sheet can be accurately cooled to a predetermined temperature at a predetermined cooling rate.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a conceptual diagram illustrating a configuration of a heat transfer coefficient estimation method in a water cooling process for a steel plate according to the present embodiment. The heat transfer coefficient is a function of the water cooling condition, and various forms have been proposed. Here, an example using the function of the following formula (1) will be described (from Non-Patent Document 1).
log (α) = A + B · log (W) + C · Ts (1)
Where α is the heat transfer coefficient
W is water density
Ts is steel sheet surface temperature
A, B, and C are parameters to be estimated.

First, calculation conditions for performing a calculation by a search method such as a simulated annealing method, which will be described in detail later, are input (step S1).
Next, initial values of the parameters A, B, and C to be estimated are input (step S2). Since the initial parameter value does not have to be an accurate value with a small error from the final value estimated in the present invention, a value obtained by a laboratory measurement so far may be appropriately input. Subsequently, the record data of the steel sheet to be water-cooled is input (step S3). Specifically, steel plate thickness, width, cooling water volume density, water temperature, plate temperature before water cooling (water cooling process entry side), plate temperature after water cooling (water cooling process delivery side), time for water cooling, etc. Enter. Here, the plate temperature is measured by a radiation thermometer, and cooling is performed while moving the steel plate in the water cooling process. Therefore, it is equivalent to input the length of the water cooling zone and the moving speed instead of the water cooling time. In this case, when the zone is divided into a plurality of areas and the water density is different, the water density for each zone is input. Moreover, when performing water cooling from both the upper surface and lower surface of a steel plate, the water density of each of an upper surface and a lower surface is input. Further, if a drainage zone is provided in the water cooling process, that is, between the water cooling zones, and the plate temperature can be measured during the water cooling, the measurement result is also input.

Next, using the conditions input in step S3 and the initial values of the heat transfer coefficient parameters A, B, and C input in step S2, for example, according to a general heat transfer calculation method as shown in the following document: Then, the plate temperature after water cooling is calculated (step S4).
"Heat transfer experiment and calculation method in continuous billet furnace", S45 / 11,
Japan Iron and Steel Institute, Chapter 5, Heat Transfer Calculation Method P68
This procedure will be described more specifically. First, among each value of the formula (1), the water density is known throughout the water cooling process, and the plate temperature at the start of water cooling is also known. Therefore, using these two values and the initial values of the heat transfer coefficient parameters A, B, and C, the heat transfer coefficient at the start of water cooling can be calculated from Equation (1). Next, from the heat transfer coefficient, the plate temperature at the start of water cooling, and the plate thickness of the steel plate, the plate width, and the water temperature of the cooling water input in step S3, a short time after the start of water cooling (for example, The plate temperature at the time when 0.1 second) has elapsed can be calculated. Using the plate temperature calculated in this way and the known water density, the value of the heat transfer coefficient at the time when the short time has passed can be calculated again from Equation (1). Thus, by calculating the plate temperature and the heat transfer coefficient one after another in short time increments, it is possible to calculate the plate temperature on the outlet side of the water cooling process.
The reason why the above calculation is repeated in short time increments is that the change in the heat transfer coefficient during that time can be ignored, and heat transfer calculation with high accuracy can be performed. Is good.

In addition, when trying to calculate the temperature of each part of the steel plate strictly, it is necessary to perform a three-dimensional heat transfer calculation for the thickness, width, and length of the steel plate. The water cooling condition is basically constant in the length direction and the temperature change in the length direction is small compared to the thickness direction and width direction. You can do thermal calculations.
Furthermore, when the water density is different for each cooling zone, it is a matter of course that the calculation is performed using the water density for each cooling zone.

  A difference between the calculated value of the water cooling process outlet side plate temperature and the actual value of the outlet side plate temperature input in step S3 is obtained as a temperature calculation error (step S5). If it is possible to measure the plate temperature in the middle of water cooling, the difference between the measured actual value and the calculated plate temperature at that point is also calculated, and the calculation error and absolute value or square of the outlet side plate temperature are calculated. By adding and adding, in addition to the entry side and the exit side, adjustment is performed in consideration of the temperature error at the intermediate point, and the accuracy of heat transfer coefficient calculation is improved.

  The processing from step 3 to step 5 is repeated by the number of the target steel plates, and the total value of the absolute values or square values of the plate temperature calculation errors is calculated (step S6). Here, when there is only one steel plate for which the heat transfer coefficient is calculated, steps S3 to S5 are performed only once, and step S6 is unnecessary, but calculation is performed based on the actual data of a plurality of steel plates. By performing the above, it is possible to perform estimation with less variation and high accuracy.

If the calculation error total value is larger than a predetermined allowable range, the values of the heat transfer coefficient parameters A, B, and C are corrected by a search method (step S7). The basic concept of the search method will be described below with respect to the local search method, which is a typical search method. First, the values of the parameters so far (in this embodiment, heat transfer coefficient parameters A, B, C) are slightly changed, and the result is evaluated (whether the temperature calculation error has increased or decreased in this embodiment). evaluate). When the improvement is obtained, the changed parameter value is adopted as the new parameter value. If no improvement is obtained, return to the previous value. This search is repeated, and the search is terminated when the evaluation result converges within a predetermined allowable range or when the calculation is repeated a predetermined number of times.
If the temperature calculation error converges within a sufficiently small allowable range, the correct heat transfer coefficient parameter is obtained at that time.

  Here, for example, when using the equation (1) as the heat transfer coefficient, the same value may be used for the parameters A, B, and C in all temperature ranges from the start to the end of the water cooling. By dividing into sections and assigning separate parameters A, B, and C to each, estimation with higher accuracy becomes possible. For example, by dividing the section into two at a steel plate temperature of about 200 degrees, more accurate parameters for the nucleate boiling area (200 degrees or less) and other areas (film boiling area and transition boiling area; 200 degrees or more) Fitting is possible.

  FIG. 2 is a diagram illustrating a procedure for estimating a heat transfer coefficient by a simulated annealing method which is one of search methods. The simulated annealing method is a method devised to compensate for the disadvantage that the evaluation value falls to the minimum value in the local search method and may not converge to a sufficiently small value. It is a technique that simulates the movement of atoms and their energy states in the process of decreasing. The local search method does not accept parameter changes that deteriorate the evaluation value, but the simulated annealing method accepts it with a certain probability. The acceptance probability is the temperature in the annealing process (it is a virtual temperature on the search algorithm, and is a value that is independent of the temperature at the time of water cooling of the steel plate that is the subject of the present invention, and is hereinafter referred to as a virtual temperature) The higher the value is, the smaller the deterioration rate of the evaluation value due to the parameter change is, and the higher the virtual temperature is, the lower the acceptance probability is. As a result, even if it falls to the minimum value, it can be expected that the virtual temperature will escape from the high temperature and converge to a parameter with a good evaluation value as the virtual temperature decreases. Hereinafter, the procedure will be described in order according to FIG. Here, the function form of the heat transfer coefficient will be described by taking the case of the above formula (1) as an example.

  First, calculation conditions and initial values of parameters A, B, and C are input (step S11). Specifically, when changing the virtual temperature, the initial virtual temperature, the final virtual temperature, the change range of the virtual temperature, the number of repetitions (how many times the calculation is repeated at the same virtual temperature), the initial values of A, B, and C And its maximum change width. The fluctuating range of the fictive temperature may be lowered in steps of a constant temperature, but the convergence is better when it is lowered at a constant ratio (for example, 0.95 times the fictive temperature of the previous time).

  Next, the values of the parameters A, B, and C are slightly changed (step S12). Here, three parameters may be changed simultaneously, or only one parameter may be changed at a time, and for example, a method of selecting it by random number calculation may be used. Further, the parameter change width is set to a value obtained by multiplying the maximum change width input in step S11 by, for example, a random number having a value in the range from −1 to +1. By taking such a procedure, it is determined at random each time which of the three parameters is changed and how much is changed.

  Based on the parameters A, B, and C calculated in step S12 and the heat transfer coefficient calculated by equation (1), the plate temperature after water cooling is calculated to obtain a calculation error from the actual delivery side plate temperature (step S13). When estimating a set of parameters A, B, and C using a plurality of steel plates, the temperature errors for all the steel plates are summed (as described in detail in steps S3 to S6 in FIG. 1).

Next, it is determined whether or not to adopt the parameter change performed in step S12 (step S14). Here, for example, it is determined as follows.
• Adopted with probability 1 when plate temperature calculation error is reduced due to parameter change • Adopted with probability Exp (−Δ / t) when plate temperature calculation error is increased due to parameter change where Δ is a parameter This is a value obtained by subtracting the plate temperature calculation error before the parameter change from the plate temperature calculation error after the change, and t is a virtual temperature. Exp (−Δ / t) takes a value close to 1 when the virtual temperature t is sufficiently high, and approaches 0 as the virtual temperature decreases. Further, the larger Δ, the smaller the value. That is, as the virtual temperature decreases, the probability of adopting the parameter change decreases, and as the plate temperature calculation accuracy due to the parameter change deteriorates, the probability of adopting the change decreases.

Steps S12 to S14 are repeated until a predetermined number of repetitions is reached (step S15). Among them, parameters A, B, and C having the smallest temperature calculation error are determined parameters at the virtual temperature, and at the next virtual temperature. Parameter initial values are set (step S16).
Next, the virtual temperature is lowered by one step (step S17). If the virtual temperature is not the final virtual temperature read in step S11, the process returns to step S12 and the procedure up to step S17 is repeated (step S18). When the final virtual temperature is reached, the procedure is terminated, and the parameters A, B, and C at that time are used as estimation results.
Here, an allowable value for the temperature calculation error may be input in advance in step S11, and the search may be terminated when the temperature calculation error becomes equal to or less than the allowable value.

  In addition, the maximum change width of the parameters A, B, and C may be a constant value in the entire range of the virtual temperature, but is set to a large value while the virtual temperature is high, and to a small value as the virtual temperature decreases. Therefore, when the virtual temperature is high, the parameter change range is large, so it converges rapidly toward the optimum value. When the virtual temperature is low, the parameter change range becomes small, so the calculation error is reduced in small increments. Therefore, it is possible to perform highly accurate estimation at a higher speed.

  In this way, if each parameter of the heat transfer coefficient can be obtained with high accuracy, it becomes possible to accurately set the cooling condition of the water cooling process so that the plate temperature after cooling becomes a specified value. That is, for the specified cooling condition, the water cooling process outlet side plate temperature is calculated by the same heat transfer calculation performed in step S4 of FIG. 1, and if there is a difference from the target temperature, the water density, Change the water cooling conditions that can be adjusted, such as the moving speed of the steel sheet, and perform the heat transfer calculation again. In this way, by obtaining a water cooling condition in which the water cooling process outlet side plate temperature matches the target temperature, and using the value to control the water cooling process, it is possible to perform highly accurate plate temperature control.

  Here, each parameter of the heat transfer coefficient is calculated in advance by the method of claims 1 and 2, and the value can be fixedly used for cooling control. As a result, if there is a difference between the temperature on the outlet side of the water-cooling process and the target temperature, the heat transfer coefficient is recalculated online, and then the value is used to influence the time-dependent change of the water-cooling equipment. The accuracy of the cooling control can be kept high.

  Hereinafter, as one embodiment of the present invention, an example of estimating a heat transfer coefficient in a water cooling process for a thick plate will be described. FIG. 3 shows the configuration of the water-cooling process experimental equipment used in this example. The whole is divided into three zones [1] to [3], and water cooling is performed from both the upper and lower sides while moving the steel plate from left to right in the figure. Thermometers for measuring the plate temperature are installed at the process entry and exit sides.

The water cooling conditions are as follows.
Steel plate thickness 20mm
Steel plate width 300mm
Inlet side plate temperature 750 degrees Outlet side plate temperature 540 degrees Time spent in each zone and the water density of the upper and lower surfaces (unit: m ³ / m ² · min)
1 zone 2 seconds Upper surface 0.3 Lower surface 0.3
2 zones 5 seconds 1.0 1.0
3 zones 8 seconds 1.0 1.0
Cooling water temperature 25 degrees Simulated annealing calculation conditions Initial virtual temperature 1000 degrees Final virtual temperature 1 degree Virtual temperature change range 0.95 times the previous virtual temperature Number of calculation repetitions at the same virtual temperature 30 times Initial value A: 2.0 B: 1.0 C: -0.001
Maximum change width A: 0.1 B: 0.04 C: 0.0001
The above formula (1) was used as the function shape of the heat transfer coefficient.

The value of the heat transfer coefficient parameter obtained as a result is as follows.
A: 2.516
B: 0.576
C: -0.00173
When the steel plate temperature after water cooling was determined for a steel plate different from the steel plate by heat transfer calculation using heat transfer parameters, an accurate calculation result with an error from the actual temperature within 10 degrees was obtained.

Moreover, the suitable water quantity density was calculated with respect to the following steel plates using the said heat-transfer coefficient parameter.
Steel plate thickness 25mm
Steel plate width 300mm
Inlet side plate temperature 750 degrees Target outlet side sheet temperature 530 degrees Cooling water temperature 25 degrees Each zone stay time 1 zone 2 seconds
2 zones 5 seconds
The results of 3 zones and 8 seconds were as follows (unit: m ³ / m ² · min).
Upper surface Lower surface 1 zone 0.5 0.5
2 zones 1.4 1.4
3 zones 1.4 1.4
When this value was used to control the water cooling process and 10 steel plates were subjected to water cooling under the same conditions, it was possible to control with high accuracy within an error of 10 degrees with respect to the target delivery side plate temperature.

It is a figure which shows the structure of the heat-transfer coefficient estimation method in the water cooling process of the steel plate of one Embodiment of this invention. It is a figure which shows the procedure which estimates a heat transfer coefficient by the simulated annealing method. It is a figure which shows the structure of the water cooling process of the Example of this invention.

Claims (3)

  In the water-cooling process of a steel plate, the steel plate is passed through a plurality of cooling zones while moving the heated steel plate and cooled to a predetermined temperature by adjusting the cooling water density in each cooling zone in order to obtain a predetermined cooling rate pattern. The surface temperature actual value, the plate thickness, the plate width, and the moving speed actual value on the inlet side and the outlet side of the water cooling process, and the cooling water temperature and the cooling water density of each cooling zone are input, and after the water cooling process is passed. The steel plate temperature from the start to the end of water cooling is sequentially calculated by heat transfer calculation for the steel plate, and the heat transfer calculation is performed using a search method so that the error between the calculated steel plate temperature and the actually measured steel plate temperature becomes small. A heat transfer coefficient estimation method in a water-cooling process of a steel sheet, wherein the heat transfer coefficient is calculated by correcting the heat transfer coefficient used in the process.   2. The heat transfer coefficient estimation method according to claim 1, wherein a simulated annealing method is used as a search method.   Using the heat transfer coefficient obtained by the heat transfer coefficient estimation method according to claim 1 or 2, the steel sheet temperature to be processed in the water cooling process is changed during and after the water cooling by changing the water cooling conditions. By repeating the above calculation, the optimum water cooling condition is determined so that the calculated steel plate temperature matches the target temperature.

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